Prove Taylor's Theorem 1.14 by following the procedure in the proof of Theorem 3.3. [Hint: Let g (t) = f(t) - P(t) - [f(2) - P(2)] . (t-x0) "+1 (x-0 ) "+1 . where P is the nth Taylor polynomial, and use the Generalized Rolle's Theorem 1.10.]